Alternative [[quality control]]<ref>Duncan AJ. Quality control and industrial statistics. Irwin 1986;pp.1-1123.</ref> (QC) procedures can be applied on a [[process]] to [[test]] statistically the [[null hypothesis]], that the process conforms to the quality requirements, therefore that the process is in control, against the alternative, that the process is [[out of control]]. When a true [[null hypothesis]] is rejected, a statistical type I error is committed. We have then a false rejection of a run of the process. The probability of a type I error is called probability of false rejection. When a false null hypothesis is accepted, a statistical type II error is committed. We fail then to detect a significant change in the process. The probability of rejection of a false [[null hypothesis]] equals the probability of detection of the nonconformity of the process to the quality requirements.
The QC procedure to be designed or optimized can be formulated as:
